Analysis: SPiM side
– The nodes of the graphs are molecules, the arrows are channels.
– As described there the procedure is to take a (huge perhaps) CRN and to reformulate it more economically, as a collection of graphs where nodes are molecules, arrows are channels.
– There is a physical chemistry model behind which tells you which probability has each reaction.
– During the computation the reactions are known, all the molecules are known, the graphs don’t change and the variables are concentrations of different molecules.
– During the computation one may interpret the messages passed by the channels as decorations of a static graph.

The big advantage is that indeed, when compared with a Chemical Reactions Network approach, the stochastic pi calculus transforms the CRN into a much more realistical model. And much more economical.

– You have one molecule (it does not matter if it is a connected graph or not, so you may think about it as being a collection of molecules instead).
– The nodes of the molecule are atoms (or perhaps codes for simpler molecular bricks). The nodes are not species of molecules, like in the SPiM.
– The arrows are bonds between atoms (or perhaps codes for other simple molecular bricks). The arrows are not channels.
– I don’t know which are all the intermediary molecules in the computation. To know it would mean to know the result of the computation before. Also, there may be thousands possible intermediary molecules. There may be an infinity of possible intermediary molecules, in principle, for some initial molecules.
-During the computation the graph (i.e. the molecule) changes. The rewrites are done on the molecule, and they can be interpreted as chemical reactions where invisible enzymes identify a very small part of the big molecule and rewrite them, randomly.